A note on essentially convex orders

被引：0
|
作者：
Bordalo, GH
机构：
[1] Univ Lisbon, Dept Matemat, P-1649003 Lisbon, Portugal
[2] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal
来源：
ALGEBRA UNIVERSALIS | 2005年 / 53卷 / 2-3期
关键词：
ordered sets; distributive lattice; embedding; join-irreducible elements; order ideal; Birkhoff's duality;
D O I：
10.1007/s00012-004-1904-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, we determine precisely which partially ordered sets (posets) have the property that, whenever they occur as subposets of a larger poset, they occur there convexly, i.e., as convex subposets. As a corollary, we also determine which lattices have the property that, if they occur as sublattices of a finite distributive lattice L, then they also occur as closed intervals in L. Throughout, all sets will be finite.
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页码：281 / 285
页数：5
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